Question: Solve for $x$ : $8\sqrt{x} + 5 = 3\sqrt{x} + 4$
Solution: Subtract $3\sqrt{x}$ from both sides: $(8\sqrt{x} + 5) - 3\sqrt{x} = (3\sqrt{x} + 4) - 3\sqrt{x}$ $5\sqrt{x} + 5 = 4$ Subtract $5$ from both sides: $(5\sqrt{x} + 5) - 5 = 4 - 5$ $5\sqrt{x} = -1$ Divide both sides by $5$ $\frac{5\sqrt{x}}{5} = \frac{-1}{5}$ Simplify. $\sqrt{x} = -\dfrac{1}{5}$ The principal root of a number cannot be negative. So, there is no solution.